The Gunners looked on course for a vital victory at the home of their fiercest rivals when Aaron Ramsey's superb flick flew past Hugo Lloris but the game changed on a red card handed to Coquelin 10 minutes after half-time.
Tottenham capitalised instantly, scoring twice in two minutes through Toby Alderweireld and a wonder-strike from Harry Kane, but then it was the hosts' turn to falter as Alexis Sanchez grabbed a late equaliser.
Coquelin's second yellow card, coming after a reckless challenge on Kane, damaged his side's hopes of a potentially crucial win in the title race and Wenger admitted it was a costly error.
"He knows he made a big mistake," Wenger said
"We knew at half-time, we warned him as well
"It was a mistake
He wanted to do well and mistimed his tackle and got sent off
I cannot complain about it
"He has to quickly learn from that
At the top level it is about full commitment and 100 per cent, but in a controlled way
When you have a yellow card it was a mistake to go down on the tackle."
Spurs dominated the opening half-hour but struggled to create any clear-cut chances and the visitors grew in confidence after Ramsey had put them in front.
A point halts the Gunners' slide following consecutive defeats to Manchester United and Swansea but they still trail Tottenham by three points in the table - with leaders Leicester arguably the game's only winners
"I feel we have shown our attitude, our character
I'm happy and proud of our performance," Wenger said.
"We refused to lose the game
We have big regrets because I couldn't see at 11 against 11 how we could drop points today.
"We made a big mistake at 1-0 but even after the shock at 2-1 we didn't lose the game and we looked dangerous going forward."
Wenger was incensed after Tottenham's Eric Dier escaped a second yellow for pulling back Olivier Giroud in the second half but Pochettino responded that Gunners full-back Hector Bellerin could also have been sent off late on.
Tottenham looked to have the momentum and the game won when Kane completed his side's turnaround and Pochettino admits his team should have held on.
"It was a missed opportunity," Pochettino said
"At 11 against 11 I think we deserved more and were unlucky in the way we conceded the goal
"The way we turned it in two minutes, then you feel a little bit disappointed, frustrated, because at 11 against 10 when you turn the result you need to keep that.
"But we are still improving and we need to move forward."
Kane arguably deserved to finish on the winning side for his stunning goal alone, which saw the striker collect the ball on the left of the penalty area before whipping it off the far post and it into the net.
It was only Kane's second goal from open play in nine matches and Pochettino was pleased to see his top scorer returning to form.
"It was a fantastic goal, amazing," Pochettino said.
"I think how he shot and scored was fantastic and I'm very pleased for him to start to score again because always strikers need to feel that."
Danny Rose was taken off in the second half with cramp in his calf
The problem is not expected to be serious, however, with a Europa League trip to Borussia Dortmund on Thursday to come.
Source : PA
Source: PA